Mathematics Commons^™

An Analysis Of Differences In Approaches To Systems Of Linear Equations Problems Given Multiple Choice Answers, Amber Lagasse

Honors Theses and Capstones

This descriptive study focuses on the approaches college students (ages 20 -24) use when solving systems of linear equations problems that have multiple choice answers. Participants were from a midsize public university in the northeast. Four approaches were considered – three forwards approaches: 1) substitution, 2) elimination, and 3) graphing, and one backwards approach: plugging in the x and y values from each multiple choice option. Participants solved systems of linear equations problems and answered questions based on their methods in a structured clinical interview. Each participant also filled out a questionnaire. It was shown from the results of this …

A Tale Of Two Workshops: Two Workshops, Three Papers, New Ideas, Gizem Karaali

Pomona Faculty Publications and Research

No abstract provided.

Ultrasonic Analysis Of Breast Tissue For Pathology Classification, Kristina Marie Sorensen

Undergraduate Honors Capstone Projects

Real time measurements may assist surgeons in obtaining negative or cancer free margins during lumpectomy to eliminate invasive re-excision. Previous findings show that high-frequency ultrasound can differentiate between a range of breast pathologies in surgical specimens. Two parameters, peak density and second-order spectral slope, are sensitive to histopathology. Our objective was to determine the mechanism linking high-frequency ultrasound to histology. The hypothesis is that ultrasound sensitivity is a function of the microscopic heterogeneity (and thus histology) of the tissue. Ultrasonic results from breast specimens were used to construct a multivariate analysis of the parameters that permitted differentiation of normal, adipose, …

The Sense-Isomorphism Theoretical Image Voxel Estimation (Sense-Itive) Model For Reconstruction And Observing Statistical Properties Of Reconstruction Operators, Iain P. Bruce, M. Muge Karaman, Daniel B. Rowe

Mathematics, Statistics and Computer Science Faculty Research and Publications

The acquisition of sub-sampled data from an array of receiver coils has become a common means of reducing data acquisition time in MRI. Of the various techniques used in parallel MRI, SENSitivity Encoding (SENSE) is one of the most common, making use of a complex-valued weighted least squares estimation to unfold the aliased images. It was recently shown in Bruce et al. [Magn. Reson. Imag. 29(2011):1267-1287] that when the SENSE model is represented in terms of a real-valued isomorphism,it assumes a skew-symmetric covariance between receiver coils, as well as an identity covariance structure between voxels. In this manuscript, we show …

Integer Solutions To Optimization Problems And Modular Sequences Of Nexus Numbers, Jeremy T. Davis

Electronic Theses and Dissertations

In this thesis, we examine the use of integers through two ideas. As mathematics teachers, we prefer students not use calculators on assessments. In order to require this, students compute the problems by hand. We take a look at the classic Calculus I optimization box problem while restricting values to integers. In addition, sticking with the integer theme, we take a new look at the nexus numbers. Nexus numbers are extensions of the hex and rhombic dodecahedral numbers. We put these numbers into a sequence, and through a few computations of modular arithmetic, we analyze the sequences and their patterns …

A Non-Parametric Approach To Change-Point Detection In Cross-Asset Correlations, L. Kaili Diamond

Electronic Theses and Dissertations

In this thesis we explore the problem of detecting change-points in cross-asset correlations using a non-parametric approach. We began by comparing and contrasting several common methods for change-point detection as well as methods for measuring correlation. We finally settle on a statistic introduced in early 2012 by Herold Dehling et.al. and test this statistic against real world financial data. We provide the estimated change-point for this data as well as the asymptotic p-value associated with this statistic. Once this process was complete we went on to use simulated data to measure the accuracy, power, and type 1 error associated with …

Compositions, Bijections, And Enumerations, Charles R. Dedrickson Iii

Electronic Theses and Dissertations

In this thesis we give an introduction to colored-compositions of an integer. This is a generalization of traditional integer compositions, and we show a few results for n-color compositions which are analogous to regular compositions with both combinatorial and analytic proofs. We also show several bijections between various types of compositions to certain types of numeric strings, and provide a generalization of a classic bijection between compositions and binary strings.

Integer Compositions, Gray Code, And The Fibonacci Sequence, Linus Lindroos

Electronic Theses and Dissertations

In this thesis I show the relation of binary and Gray Code to integer compositions and the Fibonacci sequence through the use of analytic combinatorics, Zeckendorf's Theorem, and generating functions.

A Unified Approach To Generalized Stirling Functions, Tian-Xiao He

Tian-Xiao He

Here presented is a unified approach to generalized Stirling functions by using generalized factorial functions, $k$-Gamma functions, generalized divided difference, and the unified expression of Stirling numbers defined in \cite{He11}. Previous well-known Stirling functions introduced by Butzer and Hauss \cite{BH93}, Butzer, Kilbas, and Trujilloet \cite{BKT03} and others are included as particular cases of our generalization. Some basic properties related to our general pattern such as their recursive relations, generating functions, and asymptotic properties are discussed, which extend the corresponding results about the Stirling numbers shown in \cite{HS98} to the defined Stirling functions.

There Is No Triangulation Of The Torus With Vertex Degrees 5, 6, . . ., 6, 7 And Related Results: Geometric Proofs For Combinatorial Theorems, Ivan Izmestiev, Robert B. Kusner, Günter Rote, Boris Springborn, John M. Sullivan

Robert Kusner

There is no 5,7-triangulation of the torus, that is, no triangulation with exactly two exceptional vertices, of degree 5 and 7. Similarly, there is no 3,5-quadrangulation. The vertices of a 2,4-hexangulation of the torus cannot be bicolored. Similar statements hold for 4,8-triangulations and 2,6-quadrangulations. We prove these results, of which the first two are known and the others seem to be new, as corollaries of a theorem on the holonomy group of a euclidean cone metric on the torus with just two cone points. We provide two proofs of this theorem: One argument is metric in nature, the other relies …

Finite-Temperature Dynamics Of Matter-Wave Dark Solitons In Linear And Periodic Potentials: An Example Of An Antidamped Josephson Junction, Y. Shen, Panos Kevrekidis, N. Whitaker, N. I. Karachalios, D. J. Frantzeskakis

Panos Kevrekidis

We study matter-wave dark solitons in atomic Bose-Einstein condensates (BECs) at finite temperatures, under the effect of linear and periodic potentials. Our model, namely, a dissipative Gross-Pitaevskii equation, is treated analytically by means of dark-soliton perturbation theory and the Landau dynamics approach, which result in a Newtonian equation of motion for the dark-soliton center. This reduced model, which incorporates an effective washboard potential and an antidamping term accounting for finite-temperature effects, constitutes an example of an antidamped Josephson junction. We perform a qualitative (local and global) analysis of the equation of motion. We present results of systematic numerical simulations for …

The Octonions And The Exceptional Lie Algebra G2, Ian M. Anderson

Research Vignettes

The octonions O are an 8-dimensional non-commutative, non-associative normed real algebra. The set of all derivations of O form a real Lie algebra. It is remarkable fact, first proved by E. Cartan in 1908, that the the derivation algebra of O is the compact form of the exceptional Lie algebra G2. In this worksheet we shall verify this result of Cartan and also show that the derivation algebra of the split octonions is the split real form of G2.

PDF and Maple worksheets can be downloaded from the links below.

The Secant Conjecture In The Real Schubert Calculus, Luis D. García-Puente, Nickolas Hein, Christopher Hillar, Abraham Martín Del Campo, James Ruffo, Frank Sottile, Zach Teitler

Mathematics Faculty Publications and Presentations

We formulate the Secant Conjecture, which is a generalization of the Shapiro Conjecture for Grassmannians. It asserts that an intersection of Schubert varieties in a Grassmannian is transverse with all points real if the flags defining the Schubert varieties are secant along disjoint intervals of a rational normal curve. We present theoretical evidence for this conjecture as well as computational evidence obtained in over one terahertz-year of computing, and we discuss some of the phenomena we observed in our data.

New Bilinear Estimates For Quadratic-Derivative Nonlinear Wave Equations In 2+1 Dimensions, Allison J. Tanguay

Open Access Dissertations

This thesis is concerned with the Cauchy problem for the quadratic derivative nonlinear wave equation in two spatial dimensions. Using standard techniques, we reduce local well-posedness in Fourier Lebesgue spaces to bilinear estimates in associated wave Fourier Lebesgue spaces, for which we prove new product estimates. These estimates then allow us to establish local well-posedness in a parameter range that gives improvement over previously known results on the Sobolev scale.

Sustainable Technology For Person-Centered Accessible Integrated Multimodal Information Systems, Lawrence J. Harman, Uma Shama, Heather Standring, Sabitha Gopalsamy, Anil Sadhu, Mateusz Pacha-Sucharzewski

Mathematics Faculty Publications

This paper reports on a mobility management technology project conducted by the GeoGraphics Laboratory at Bridgewater State University in Bridgewater, Massachusetts, in the Northeastern United States (U.S.). This study is a part of a much larger mobility management technology deployment by the Cape Cod Regional Transit Authority (CCRTA) that deployed integrated intermodal intelligent transportation system (ITS) to support the mobility of a metropolitan region that has a high proportion of elderly residents and persons with disabilities and is a significant tourist destination for national and international travelers. This paper reports on a research project that is developing smartphone applications to …

270: How To Win The Presidency With Just 17.56% Of The Popular Vote, Charles D. Wessell

Math Faculty Publications

With the U.S. presidential election fast approaching we will often be reminded that the candidate who receives the most votes is not necessarily elected president. Instead, the winning candidate must receive a majority of the 538 electoral votes awarded by the 50 states and the District of Columbia. Someone with a curious mathematical mind might then wonder: What is the small fraction of the popular vote a candidate can receive and still be elected president? [excerpt]

Mathematical Problem Posing As A Measure Of Curricular Effect On Students' Learning, Jinfa Cai, John Moyer, Ning Wang, Stephen Hwang, Bikai Nie, Tammy Garber

Mathematics, Statistics and Computer Science Faculty Research and Publications

In this study, we used problem posing as a measure of the effect of middle-school curriculum on students' learning in high school. Students who had used a standards-based curriculum in middle school performed equally well or better in high school than students who had used more traditional curricula. The findings from this study not only show evidence of strengths one might expect of students who used the standards-based reform curriculum but also bolster the feasibility and validity of problem posing as a measure of curriculum effect on student learning. In addition, the findings of this study demonstrate the usefulness of …

Analyzing Multiple-Probe Microarray: Estimation And Application Of Gene Expression Indexes, Mehdi Maadooliat, Jianhua Z. Huang, Jianhua Hu

Mathematics, Statistics and Computer Science Faculty Research and Publications

Gene expression index estimation is an essential step in analyzing multiple probe microarray data. Various modeling methods have been proposed in this area. Amidst all, a popular method proposed in Li and Wong (2001) is based on a multiplicative model, which is similar to the additive model discussed in Irizarry et al. (2003a) at the logarithm scale. Along this line, Hu et al. (2006) proposed data transformation to improve expression index estimation based on an ad hoc entropy criteria and naive grid search approach. In this work, we re-examined this problem using a new profile likelihood-based transformation estimation approach that …

Sample Path Properties Of Volterra Processes, Leonid Mytnik, Eyal Neuman

Communications on Stochastic Analysis

No abstract provided.

Stochastic Calculus For Gaussian Processes And Application To Hitting Times, Pedro Lei, David Nualart

Communications on Stochastic Analysis

No abstract provided.